Design optimization of chirped FBG as a dispersion compensator

8/13/2019 Design optimization of chirped FBG as a dispersion compensator

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Design optimization of chirped FBG as a dispersion

compensator

D. Aneesh1, A.Vishnu Vardhanan

2, and R.Gangopadhyay

3

Dept. of Electronics and Electrical Communication Engineering

Indian Institute of Technology, Kharagpur

E-mail: [email protected], [email protected], [email protected]

Abstract:Chirped fiber Bragg grating (FBG) provides an

attractive solution for low cost dispersion compensation

in a fiber optic transmission system. The present work

carries out the design optimization of a chirped FBG in

respect of chirp bandwidth and apodisation profile in

achieving optimum dispersion compensation in a

40Gbps optical transmission link for differentmodulation formats.

1. Introduction:Linearly chirped fiber Bragg gratings are commonly usedfor dispersion compensation in 10Gbps optical transmission

systems. The availability of mass production techniques and

low cost has made this device very attractive for dispersion

compensation. Even in higher bit rates such as 40Gbps case

they are also found to be very effective.

The performance of a chirped FBG is controlled by several

parameters such as the length of the grating used for

compensation, chirp bandwidth, apodisation profile, acindex modulation depth and the number of uniform steps in

the grating. Several studies are carried out to optimizedesign procedure for dispersion compensating chirped FBG.

The critical parameters for the design of a chirped FBG used

as dispersion compensator are the grating length, chirped

bandwidth and the apodisation profile. Conventional

approach for choosing the length of the grating ( Lg ) basedon the knowledge of the signal bandwidth and amount of

the fiber dispersion to be compensated. Such a procedure

needs adhoc trial of fixing the length of the grating to be2Lg, 3Lg etc in order to achieve the best performance.

However this approach does also consider how different

modulation formats may require the FBG lengthoptimization.

The present procedure determines the choice of the FBG

length based on appropriate selection of chirped bandwidth

containing a desired level of signal energy Ethdepending on

the performance optimization required. It is known thatoptimization of apodisation profile has a distinctive role in

ensuring minimum delay ripple across the gratingbandwidth. As per current literature the symmetric tanh

apodisation is claimed to be the best apodisation profile. In

the present study we show that further design optimizationcan be effected if one uses asymmetric tanh apodisation.

.

2. Design Procedure Optimization

and SimulationA number of parameters are involved in the design of a fiber

Bragg grating. The design of chirped FBG for dispersion

compensation requires proper choice of various gratingrelated parameters. The following steps are involved in the

design.

1) Calculate the grating length as

=

nBDLL fg

2

2

(1)

Lf is the length of the fiber, D is the fiber dispersion

parameter (ps/nm/km), B is the signal bandwidth, is the

central wavelength and n is the effective refractive index.

2) For a given length Lg the number of uniform sections ischosen to be 60 or higher. The grating simulation is carried

out by transfer matrix approach [6] for an adequately chosenvalue of the chirp bandwidth, neff=1.45, ac modulation index

at optimized value 1.2x10 -4 an and appropriate apodisation

profile (tanh) to maintain a desired accuracy and the

performance targets.

3) For a chosen value of the chirped bandwidth it is further

necessary to optimize the grating length to be 2Lg, 3Lg etc.

in order to achieve the optimum result.

It may be noted that the above choice of length also varies

depending on the signal modulation used. This may beappreciated referring to Table 1 which shows that for the

eye opening penalty (EOP) of 0.2 dB for the dispersion

compensated 40Gbps signal at the output of the grating, the

grating length differs depending on the value of the chirp

bandwidth and the modulation format. The above designprocedure suffers because the choice of chirp bandwidth

does not actually take into account the detailed nature of the

signal spectrum.


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Table1: FBG parameters for an EOP of 0.2 dB for different

modulation formats:

ModulationFormat Length(cm)

ChirpBandwidth(nm)

NRZ 10.00 0.8

21.00 1.6

RZ 20.30 1.6

26.30 2.0CSRZ 10.29 0.8

20.68 1.6

2.1 Present Design approachIn this design we tried to optimize the design in

terms of the length of the grating, chirp bandwidth and

apodisation. For all other parameters standard values are

adopted. DC index modulation of zero and AC indexmodulation of 1.2x10 -4 are taken for all the cases. Number

of steps in the calculation of grating is chosen to be 100.

Length optimization:The choice of Lg can be simplified by taking B in (1) as the

chirp bandwidth of the dispersion compensator. The

interdependence of parameters in the past design andambiguity can be removed by this method.

In order to find out the amount of chirped bandwidth neededfor effective compensation we consider the bandwidth

containing energy above a certain threshold. For example

Table2 shows the energy content in a specified bandwidthfor different modulation format. Based on the required EOP

one can choose the signal bandwidth containing energy

greater than the threshold. Based on this value of chirp

bandwidth the grating length is calculated using (1).

The above approach is used for the simulation based designof the chirped FBG for dispersion compensation. In the

simulation a PN sequence of length 26-1 at 40Gbps isgenerated which is used to produce a modulated signal

(NRZ, RZ and CSRZ) from the Mach Zahnder modulator.

The output from Mach Zahnder modulator is coupled to a

single mode fiber (D=16ps/nm/Km). The received output isfiltered by an optical Bessel filter (3dB

bandwidth=160GHz) and after photo detection is filtered by

an electrical filter (3dB bandwidth= 28GHz). Split step

Fourier method is used to simulate the propagation through

the fiber and transfer matrix method [6] is used forsimulation of the Bragg grating.

The performance result of grating is expressed in terms ofEOP vs chirp bandwidth for different modulation formats.

As one finds from Fig. 1 that depending on the modulation

format appropriate chirp bandwidth needs to be utilized in

the design for obtaining required EOP. It is also found fromsimulation that for an EOP of 0.2 dB the required energy

threshold Eth =98%, 96% and 98% for NRZ, RZ and CSRZ

respectively.

Figure 2 also depicts the EOP performance with fiber lengthfor two different values of chirp bandwidth providing

different levels of energy for NRZ signaling format.

Table2. Energy content in a given signal bandwidth

Percentage energy in a Bandwidth

( Eth)SignalBandwidth NRZ RZ CSRZ

0.6 97.63 61.04 97.37

0.8 97.81 87.30 98.25

1 98.47 89.63 99.08

1.2 98.78 90.21 99.75

1.4 98.81 90.30 99.85

1.8 99.18 91.05 99.91

2 99.20 94.09 99.96

3 99.50 95.12 100

0

2

4

6

8

10

0 2 4

Chirp Bandwidth (nm)

EOP(dB)

NRZRZCSRZ

Fig. 1. EOP variation of EOP for different chirp

Bandwidth at 40Gbps

0

0.5

1

1.5

2

2.5

70 75 80 85 90

Fiber Length (Km)

EOP(dB)

E=95% chirpBW=0.6nm

E=99% chirpBW=1.6nm

Fig. 2. EOP performance with distance for different chirp bandwidth

providing different levels of energy for NRZ at 40Gbps


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Apodisation Optimization:Several investigations have been carried in the past out to

find out the best apodisation profile for sidelobe suppression

and improved time delay ripple performance [3] [7]. In

literature it is found that symmetric tanh is the best known

apodisation among these. We show here that further gratingimprovement can be effected if asymmetry is introduced in

the tanh apodisation profile:

( )( )

=

LzkLL

zLb

kLzL

az

xf

,2

tanh

0,2

tanh

..(2)

where a and b are tanh window parameters and k is

asymmetric apodisation parameter.

Fig. 3. Asymmetric apodisation profiles

Figure 3 shows several asymmetric apodisation profilesalong the grating length for different values of a, b and the kvalue varies in the range of 0.1 to 0.9. The impact of the

slope asymmetry on both EOP and mean time delay ripple is

shown in Figure 4. Compared to symmetric tanh profile

asymmetric tanh profile provides significant improvement

of grating performance.

0

0.2

0.4

0.6

0.8

1

0 0. 1 0 .2 0 .3 0. 4 0 .5 0. 6 0 .7 0 .8 0. 9 1

Apodisation asymmtery(k)

E

OP(dB)

0

5

10

15

20

25

Averagetim

edelay

ripple(ps)EOP

Avg.time delay

Fig4.EOPand average time delay ripple versus apodisation asymmetry for

NRZ at 40Gbps

0

0.51

1.5

2

2.5

3

3.5

4

70 75 80 85 90Fiber Length ( Km)

EOP

(dB)

tanh a=4 b=4 k=.5

tanh a=2 b=7 k=.8

Fig. 5.Comparison of EOP for asymmetric and

symmetric apodisation

3. Conclusion

A simple easy-to-use design optimization of chirped FBG asdispersion compensator is presented. In particular, the

criterion for appropriate choice of the chirp bandwidthbased on threshold energy of the signal allows the

determination of grating length automatically optimized.

The procedure also easily accommodates length

optimization for different modulation formats. Further,better length optimization can be achieved by introducing

slope asymmetry in conventional tanh apodisation resulting

in both decreased passband delay ripple and reduced EOP.

References

[1] P.Fernandez, J.C. Aguado, J.Blas, R.Duran, I.deMigfuel, J.Duran, R.M. Lorenzo and E.J. Abril,Analysis and Optimisation of the apodisation sharpness

for linearly chirped dispersion compensation gratings,IEE proc-Optoelectronics, pp-69-73, April-2004.

[2] D. Pastor, J.Capmany, D. Ortega, V. Tatay and J. Marti ,Design of apodized linearly chirped fiber grating fordispersion compensation, J.of Lightwave Technology,

pp-2581-2588, November 1996.

[3] K.Ennser, M.N. Zerva and R.I. Laming, Optimization

of apodised linearly chirped fiber grating for opticalcommunications, IEEE J. of quantum technology, pp-770-777, May 1998.

[4] K.Ennser, R I Laming and M.N. Zerva, Analysis of

40Gbps TDM-Transmission over Embedded StandardFiber Employing Chirped Fiber Grating DispersionCompensators, J.Lightwave Technology, pp 807-811

May 1998.


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[5] F. Ouellette, Dispersion cancellation using linearly

chirped Bragg grating filters in optical waveguides,Optics Letters, pp 847-849, October 1987.

[6] Raman Kashyap, Fiber Bragg Grating, Sen Deigo,Academic Press, 1999.

[7] M.N. Zervas and D.Taverner, Asymmetrically apodized

linearly chirped fiber Bragg gratings with improveddispersion characteristics, ECOC98, September 1998.

Design optimization of chirped FBG as a dispersion compensator

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